In a large bowl, mix the vinegar, lime juice, garlic, salt, and pepper. Place the chicken pieces in the mixture, and marinate at least 15 minutes.
Heat the oil in a large skillet over medium heat. Transfer the chicken and marinade to the skillet. Cover, and cook chicken about 10 minutes.
Mix the green pepper, onion, tomatoes, and ketchup into the skillet, cover, and continue cooking 15 to 20 minutes, until chicken is no longer pink and juices run clear.
